The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X X X X X 1 X 1 X X X 1 1 1 X 0 X 1 X X 1 X 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X X X X X 0 X X X X 0 0 0 X X 0 X X 0 X X X X 0 X 0 0 X 0 X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X 0 X 0 X 0 0 X 0 X X X X 0 0 X X 0 X X 0 0 X X X X X 0 X 0 0 0 0 X X 0 X X 0 X 0 X 0 X 0 0 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 X 0 X X 0 0 X 0 X X 0 0 X 0 X 0 X 0 X 0 X X X X X X X X 0 0 0 X X 0 0 X X X 0 0 0 X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 X 0 X 0 0 X X X 0 0 X 0 0 X 0 X X 0 0 0 X 0 X 0 X X X 0 X 0 0 0 0 X X X 0 X X 0 X X X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 0 0 0 X 0 0 X X 0 0 0 0 X 0 0 0 X 0 X 0 0 0 X 0 X X 0 X 0 X 0 X X X X 0 0 X X X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 X X X 0 X 0 X 0 X 0 0 0 0 X 0 X 0 X 0 X X 0 0 X X X 0 0 X X X 0 0 X X 0 X 0 0 X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 X X X X X 0 X 0 X X 0 0 0 X X 0 0 0 X 0 0 0 X X 0 X 0 X 0 X X X 0 0 0 X X X X 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X 0 0 X 0 X X X 0 0 X 0 0 X 0 0 X 0 0 X 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X 0 X X X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X 0 X 0 X 0 0 X X X 0 X 0 X X 0 X X X X X 0 X X 0 X X 0 X X X 0 X 0 0 0 X 0 X X X X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 X X X 0 0 X X 0 X X X X X X X X 0 0 0 0 0 X 0 0 X 0 X 0 0 0 0 0 0 0 X 0 X X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 0 0 0 0 0 X X 0 X X 0 X 0 0 X X X X 0 0 0 X X X 0 X X 0 0 X X 0 X X X X 0 0 X 0 0 0 X 0 X generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+207x^68+435x^72+30x^74+705x^76+280x^78+1041x^80+726x^82+1391x^84+704x^86+1088x^88+266x^90+669x^92+40x^94+345x^96+2x^98+186x^100+64x^104+10x^108+1x^112+1x^136 The gray image is a linear code over GF(2) with n=168, k=13 and d=68. This code was found by Heurico 1.16 in 47.4 seconds.